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woensdag 1 juni 2016

On a cold winter day, 21 November 1934, professor
Vening Meinesz turned on his pendulum apparatus. Just a few minutes ago, the
submarine K-XVIII dived to a depth of 30 meters [1]. At these depths, the motion of the surface
waves was dampened such that it did not influence the delicate
measurements done by the professor. This particular observation would mark the 500th measurement, observing the tiniest changes in the Earth's gravity field. This
new gravity dataset would reveal many new mysteries of our home planet and would be
the life’s work of Vening Meinesz. It is all documented in scientific
publications of four volumes called Gravity Expeditions at Sea,
followed by a fifth volume with gravity observations done by his students.
Along these expeditions, the professor had brought his specially designed
pendulum apparatus, or folklorised by the sailors on board the many submarines:
Het Gouden Kalf (the Golden Calf).

The pendulum apparatus of Vening Meinesz, also known as "Het Gouden Kalf" (the Golden Calf). Positioned on the left side is the protective casing with the recording instrument on top. On the right side is the pendulum apparatus with the three pendulums at the back.

During the beginning of 1900, Earth's gravity field
was only measured on land. The classical single-pendulum device needed a stable
platform, which was impossible to achieve on ships. The swell and the shaking
of the large engines made it impossible to keep the pendulum stable. Therefore,
73 percentage of the Earth's gravity field was yet unknown to the geodetic
community. A young civil engineer from the Technische Hogeschool in Delft
would change this. After his graduation in 1915, Felix Andries Vening Meinesz,
son of a mayor of Rotterdam and Amsterdam, was given the task at the Rijkscommisie
voor Graadmeting to set up Holland’s first gravimetric base station
network. For this project he needed a device that could measure the gravity
field with the highest accuracy possible, which in those days were pendulum
instruments. Unfortunately, he found out that the soil of the Netherlands was
very unstable. The waves of the North Sea, when smashed at the dunes of the
Dutch coast, would generate solid waves in the soils that affect the motion of
the pendulum when observing in Delft.

Professor Vening Meinesz changed his location of
research to a small town called de Bilt. In particular, he moved to the KNMI
(Royal Dutch Meteorological Institute). Here, in the basement of the KNMI
building at the Kloosterweg, underneath the office of the director of the
institute, Van Everdingen, Vening Meinesz commenced his measurements and
thorough calibrations with new type of pendulum instruments [2]. Evidence of
his presence can still be found at the old KNMI building, where a historical
plaque indicating the gravimetric base station is still present on the left rail
of the concrete stairs on the west side of the building. The location at the
KNMI was in particular useful for Vening Meinesz, because the geological
subsurface made it a very stable environment for gravity observations. Due to
the stable subsoil, external motions were dampened and the remote location
would decrease the oscillation of lorries and inland shipping. The extreme
stable surroundings made it possible for the professor to test and calibrate
his equipment with extreme precision, resulting in very accurate measurements
of the gravity field later during his expeditions at sea [3].

Geodetical plague of the gravity measurement at the old building of the KNMI, marking the location of the gravimetric reference point.

Due to the success of his work in the Netherlands
removing external accelerations from the measurements, Vening Meinesz decided
to try measuring on board a surface ship. Unfortunately, the motion of the
waves and the shaking due to the steam engine were too severe and the observations
were worthless. Vening Meinesz, slightly disappointed, presented his negative
results in Maastricht at the 19th Nederlandse Natuur- en Geneeskundig
Congres. After his presentation, Ir. F.K.Th. van Iterson (1877 -
1957), director of the Staatsmijnen, suggested to use submarines instead
of surface ships [4]. Wave motion at 30 meters depth would be dampened and
submarines use quiet electro-motors when diving. This touch of serendipity was
the start of many submarine gravity expeditions at sea.

Improving during submarine expeditions - the true
engineering spirit

The Golden Calf did not have its final form from the
beginning. Vening Meinesz, being a true engineer, modified the apparatus many
times during his numerous submarine voyages, always improving the design.
During his work on gravimetric reference network of the Netherlands, the professor
used the Von Sterneck-Stückrath gravimeter (1887), but it proved to be
difficult to operate during the long K-II submarine expedition (1923). Vening
Meinesz decided to design a new gravimeter from the experience during this
expedition. He ‘cannibalised’ the pendulums of the old Von Sterneck
gravimeter (the casing of the old Von Sterneck was in 2015 still in possession
of the KNMI). Vening Meinesz used the principle of the Von Sterneck gravimeter
to acquire high precision. However, his mathematical analyses of the pendulum
motion showed that he only needed three pendulums for two independent
measurements instead of four [5]. The pendulums were placed in an along-direction
pair-wise configuration. One pair of pendulums would produce an independent
gravity observation. This was done to eliminate any external horizontal motion. The
differential equation to describe a pendulum’s motion attenuated by a
horizontal acceleration is as follows:

The angle of deflection of the pendulum is represented
by θ, whereas the length is l and gravity is noted by g. The horizontal acceleration is given
by ay. With one pendulum
it is impossible to decouple the value of g
from the external accelerations acting on the instrument. Therefore, two
pendulums are used, where the difference of their deflection angles is
measured. The external acceleration, which is similar for both pendulums, is
then mitigated by subtraction.

The pair θ1-θ2is observed by an ingenious design of light rays, mirrors and prisms on the
top of the pendulum apparatus. This second-order differential equation is easy
to solve. For small initial amplitudes of the virtual pendulum, this will
result in the famous pendulum relation of Christiaan Huygens:

The period of the virtual pendulum (T1-2)
can be determined from the recordings of the light rays. The recording
instrument, a small ‘dark chamber’ with photographic roll of paper, was
situated on top of the pendulum casing. A clockwork contraption unrolled the
photo paper during the observations, such that the defections of the pendulum
pair were recorded.

Top view of the pendulum apparatus illustrating the locations of the three pendulums. The coloured dashed lines depict the path of the light rays from the recording apparatus. Red and green show the recording of the motion of two paired-pendulums, whereas blue depicts only the recording of the middle pendulum. The yellow light ray was observing the tilt and temperature changes of the instrument.

This unrolling of the photographic paper was not
accurate enough, so Vening Meinesz designed another approach to accurately
determine the time periods of the pendulum. The professor always took the state-of-the-art
chronometers on board the submarine expeditions. One chronometer, the Nardin
212, was taken on almost all the expeditions and was accurate up to 0.04
sec/day. He asked for alternations made to the chronometers, such that they
were able to open and close an electrical circuit every 0.5 seconds. The electric pulse was then used to control a shutter in the recording instrument
to shortly interrupt the light ray. This resulted in small 0.5 markings in the
final recording sheets and could be used to determine the time period with
extreme accuracy.

During the submarine expeditions, Vening Meinesz
always kept alternating the device and improving on its accuracy. The smallest
details were taken into account. For example, when the submarine dived to 30
meters depth, the pressure of the air inside the enclosed vessel increased with
sudden temperature changes of a few degrees. Because the Golden Calf had
thermal insulation in the form of sheep’s wool, the air temperature inside the
pendulum apparatus did not experience these sudden changes. However, during the
45 minute long observations, gradually the temperature would change due to
leakages in the cover. In turn, this would effect the very sensitive
measurements. A small electric heater in the bottom of the device would be turned
on before the dive to heat up the air a few degrees to simulate the
temperature of the air after dive. In this way, during the dive there would be
no temperature offset between the air in the submarine and inside the pendulum
device. It needed some practice of the operator, but it was effective.

A 3D computer model of the submarine Hr. Ms. K-XVIII made from the old engineering drawings of the shipyard Fijenoord

The name "Golden Calf" was given to the
pendulum apparatus by the submarine crew. The story goes that during the
gravity observation all the non-essential personnel had to lie down in their
bed-bunk to create a very stable submarine. The Dutch Navy declared that
this was a degradation of personnel life and well-being and therefore paid the
submarine crew 1 guilder (currency of the Netherlands at the time) per dive
extra wage for compensation. So, when the crew members saw the pendulum
apparatus carried on board, they rubbed their hands and cheered on the coming
of the Golden Calf, because this meant good wages. Of course, the bronze
platting will have had some influence in the creation of the name. The abundant
use of bronze in the casing has given it a gold colour, which could also lead
to the name Golden Calf.

Results and legacy

One of the well-known theories of Vening Meinesz is
his model to explain the stable situation of continents, mountains, and
volcanic islands. Previous researchers assumed that these large masses
were floating on a liquid mantle, like an iceberg floats in the water. From the observations with the Golden Calf, Vening Meinesz could deduce that
the solid crust was partially responsible for holding up the mountains. Gravity
observations of coastal regions and volcanic islands showed that the crust
acted as a plate and experienced elastic bending due to the loading of the
extra topography. This theory is now called Vening Meinesz isostasy and is
especially successful in explaining the gravity field of oceanic islands.

Old gravity results from Vening Meinesz of Indonesia (top) compared with current knowledge of the gravity field (bottom) from combined ground, seaborne, airborne, and satellite gravimetry. Please appreciate the accuracy that Vening Meinesz already obtained almost 100 years ago.

The Golden Calf revealed many secrets of the deep
ocean. For example, the gravity signal at the Mid Atlantic Ridge differs from
the gravity anomalies at the famous Vening Meinesz belts (now known as
subduction zones). Vening Meinesz found strong negative and positive gravity
anomalies situated parallel to the volcanic arc in the East Indies (Indonesia),
which could not be explained by isostasy. This indicated a dynamic process
along the southwest shore of the East Indies. Similar gravity anomalies were
found in the West Indies, where Harry Hess, a young American scientist, was
responsible for most of the gravity surveying. Harry Hess is mostly known for
the founding father of the geophysical model for the spreading ridge, which occurs at the Mid Atlantic Ridge [6]. This
model is believed to be the first step in accepting the tremendous powerful
theory of plate tectonics. At the time of Vening Meinesz this was not
yet known and both subsurface structures showed similar volcanic geology and seismic
activity, but because of the different gravity anomalies Vening Meinesz and
Harry Hess knew that different geological processes were at play. Other
results thanks to the Golden Calf and Vening Meinesz were the first gravity
measurements of a transform fault, the Romanche Trench (at the time theorised
as volcanic craton). Also, the gravitational signatures of subsurface
structures like the Walvis Ridge and the Rio Grandes Rise were observed during
the submarine expeditions.

Up until 1960, the Golden Calf was the only instrument
that could measure the gravity field with such precision. One of the last
scientific expeditions with the instrument was made in 1960 [7], to measure the
gravity field in the South Atlantic and Indian Ocean. The instrument was
succeeded by the Graf-Askania gravimeter, which was a spring gravimeter on a
stable platform [8]. Overall, the Golden Calf was responsible for 37 years of
ocean gravimetry.

The original Golden Calf is now in possession of the
TUDelft Library, section Heritage. The apparatus is loaned to the museum of TUDelft,
the Science Centre, where it will be placed in the geodesy section, such that
the public can enjoy the beauty of this incredible contraption. In
2014-2015, a project group from TUDelft documented and studied the voyage of
Vening Meinesz on board the K-XVIII, where special attention was given to the
Golden Calf and its measurement principle. The project was developed under the
larger Expedition Wikipedia project. The results of that project can be found
on an interactive website: expeditiewikipedia.nl/#vening-meinesz